Document Type : Original Article
Authors
 Fariborz Fazelipour ^{1}
 Shahin Alizadeh ^{1}
 Abolfazl Mohammadi ^{} ^{} ^{2}
 Alireza Bozorgian ^{} ^{3}
^{1} Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
^{2} Department of Chemical Engineering, University of Bojnord, Bojnord, Iran
^{3} Department of Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran
Abstract
Gas treatment procedures play a crucial role in eliminating acidic gases from natural gas and other hydrocarbon streams. Within the confines of this investigation, we propose an innovative methodology that employs the eCPA equation of state to prognosticate the solubility of hydrogen sulfide (H_{2}S) in aqueous solutions containing Nmethyl diethanolamine (MDEA), monoethanolamine (MEA), and diethanolamine (DEA). The electrolyte Cubic Plus Association (eCPA) equation of state takes into account six vital parameters, encompassing the molecular size, configuration, and polarity of the constituents, to accurately anticipate the equilibrium treatment of H_{2}S absorption in various conditions.
The results acquired from the experimental assessment of H_{2}S solubility were juxtaposed with those derived from modeling, revealing a commendable concordance amidst the respective data. In order to gauge the accuracy of the projected model, we employed the absolute average relative deviation (AARD%) as a statistical errorindex. The experimental data procured in this study exhibited an acceptable validation in accordance with the outcomes of modeling endeavors.
The performance evaluation reveals that, within the temperature range of 25140 °C, acid gas loadings of 01.6 (mol gas/mol solution), and aqueous alkanolamine amounts of 1549 wt. %, the absolute average relative deviation (AARD%) remains consistently below 4.5%. This emphasizes the reliability and efficiency of our model in accurately predicting H_{2}S solubility under diverse operating conditions.
Graphical Abstract
Keywords
Main Subjects
Introduction
Major acid gases, including Hydrogen sulfide (H_{2}S) and carbon dioxide (CO_{2}), are often required to be eradicated from flue gases and other resources. In the petroleum industry, acid gases like H_{2}S should be separated roughly totally from gas streams because of their toxicity and corrosiveness to prevent catalyst poisoning in refinery operations. One of the most common approaches for removing acid ingredients is using an aqueous alkanolamine solution during the reactive absorption processes [1]. The presence of an alkanolamine drastically affects the acid gas solubility in water. Acidic gases reach equilibrium in the vapor phase with the unreacted molecular form of the same acid gas in water. At equilibrium, the untreated acid gas solubility in an aqueous solution containing a reactive solvent is governed by the partial pressure of that gas above the liquid. If the gas reacts in the aqueous phase to form nonvolatile products, additional gas can be solubilized at a given acid gas partial pressure [2].
The hydrogen bonding with water that forms by hydroxyl group in the alkanolamine structure enhances the amine solubility in water and also the amine solution's surface tension, and hence raises the numbers of hydroxyl functional group, which could barricade amine loss from the volatility of the amine [3]. The amino group presents high reaction rates, while tertiary amines have mangy response rates and H_{2}S through acidbase catalyst mechanism and shape bicarbonate ions. Nevertheless, it needs a high quantity of energy compared to bicarbonate in the regeneration of the amine solution [3,4]. Sterically alkanolamines have been recommended as potential solvents for H_{2}S absorption because they attain dangerous circumstances that without difficulty transform to bicarbonate and emit free amine molecules through the hydrolysis reaction, resulting in high rates of response like other early amines, considerable H_{2}S absorption capability and lower energy for tertiary amines [3,5]. The group of hydroxyl and steric hindrance in the structure of amine influence the capacity of H_{2}S absorption. As a result, alkanolamines significantly enhance the acid gas solubility in the aqueous phase [3].
The functional tertiary amine for removing acid gas is methyl diethanolamine (MDEA). Its low vapor pressure, low corrosion rate, relatively low regeneration heat, and selective removing H_{2}S from approach streams, including CO_{2} [6]. Both Monoethanolamine (MEA) as a primary amine, and diethanolamine (DEA) as a secondary amine, have been the most widely employed gastreating alkanolamine agents during the last several decades [711]. MEA, DEA, and diglycolamine (DGA) react rapidly with H_{2}S and CO_{2} in the aqueous phase. H_{2}S in water is a Bronsted acid, and alkanolamines solutions are Bronsted bases. Hence, H_{2}S reacts with all alkanolamines in the aqueous phase through a highspeed proton transfer mechanism. This reaction is essentially characterized by an immediate mass transfer [12]. Because of enhancing the absorption rate affected by MEA and DEA in aqueous solution, these solvents remove trace quantities of H_{2}S and remove a minor fraction of the CO_{2}. Therefore, they are used in applications wherein it is necessary to remove the bulk fraction of CO_{2} and H_{2}S from a gas stream to very low levels. The drawback of using MEA, DEA, or DGA for gas treating is that the reactions between these amines and H_{2}S or CO_{2} are highly exothermic. As a result, gas treating applications that employ aqueous alkanolamine solvents require a substantial input of energy in the stripper to replicate the reactions and bare the acid gases from the solution. In the ternary system of H_{2}OH_{2}SMEA, H_{2}OH_{2}SMDEA and H_{2}OH_{2}SDEA systems, there is a possibility of forming hydrogen bonds between each molecule itself and adjacent molecules, which results in the association among molecules. Also, the ionic types exist in the liquid phase due to the reactions during the absorption of hydrogen sulfide by alkanolamine. Consequently, these systems are among the electrolyte and the association systems. To model such methods, the electrolyte cubic plus association (eCPA) equation of state (EoS) is usually required [13,14]. This is because eCPA EoS can consider both effects of ionic species and association molecules that have the capability of forming hydrogen bonds.
Phase equilibrium in the absorption of acid gases like H_{2}S and CO_{2} is a significant subject for efficient planning of the gas sweetening process [1520]. For planning the sweetening process, the data on acid gas solubility in amines at various states are required. The scope of this study is thermodynamic modeling of equilibrium solubility of H_{2}S in aqueous MDEA, MEA, and DEA solution by eCPA equation of state. The model should be able to model condensate, gas, and amine equilibrium (VLLE) in a constant method [21]. Calculations of the vaporliquid equilibrium model presented in this study are based on chemical and phase equilibria. Phase equilibria affect the chemical equilibria and vice versa. The chemical equilibrium is used for molecules and ions, and the vaporliquid phase equilibrium is used for molecules because ion species are nonvolatile. They are presented only in the liquid phase. Countless works about modeling the gas sweetening process can be found in the literature. The equilibrium solubility of H_{2}Salkanolaminewater systems was calculated by Kent and Eisenberg [21]. They opted for the exported equilibrium constants from the literature for any reaction except the pretension and carbamation. They dealt with these two parameters as tunable parameters and compelled the relentless pressure to adapt the experimental data. The proposed model is reliable in the bounded loading ranging between 0.2 and 0.7 (acid gases mol/amine's mol). In addition, Kent and Eisenberg's model is simple and does not include the nonideality of ionic and molecular species. Austgen Jr [22] adopted the electrolyteNRTL model for alkanolamineacid gas systems. An accurate thermodynamic plan had been modified. The tunable parameters containing the ternary (moleculeion pair) interaction parameter and double interaction parameters had deteriorated to coordinate ternary systems, including acidgas, amine, water, and dual systems, including aminewater. They also adapted the carbamate composure consistent in their estimation. Forecasting blended acid gases in aqueous amines, and CO_{2} in aqueous amine blends were also produced. However, the utilized parameters in binary and ternary interaction differed in some systems. Huttenhuis et al. [23] combined the Born term with the model given by Fürst and Renon [24] for liquidvapor computation of CO_{2} −MDEA−H_{2}O −CH_{4} systems. In addition, they have expanded their eEoS to portray the solubility of mixed CO_{2}, H_{2}S, and CH_{4} in MDEA aqueous solutions. Zoghi and Feyzi [25] presented a model to calculate the solubility of CO_{2} in the aqueous solution of Nmethyl diethanolamine. They improved electrolyte EOS proposed by Huttenhuis et al. [23] by adding association terms. They used a modified PengRobinson EoS as a cubic term of the EOS, a comparative study of modeling (for the first time), and experimental evaluation of solubility of H_{2}S in the aqueous solution MEA, MDEA, and DEA were carried out using eCPA EoS. In a parallel effort, researchers such as Skylogianni et al. (2020) explored the solubility behavior of hydrogen sulfide in MEA solutions. The study highlighted the influence of temperature, concentration, and other factors on H_{2}S solubility, contributing to a more comprehensive understanding of the underlying thermodynamics [26]. Shirazi and Lotfollahi investigated different association schemes (2B, 3B, and 4C) for water (H_{2}O), MDEA, and H_{2}S in the PCSAFT EoS. The developed ePC_SAFTMB EoS shows promise in modeling the solubility of H_{2}S in aqueous MDEA solutions, with the incorporation of Born and MSA terms enhancing predictive accuracy [27]. In 2020, Shirazi et al. studied the PCSAFT equation of state to determine the solubility of hydrogen sulfide in a normal methyldiethanolamine aqueous solution. The developed model can predict the equilibrium solubility of hydrogen sulfide across a temperature range of 298 to 413 K and a pressure range of 0.0013 to 5840 Kpa [28]. This study aims to conduct systematic thermodynamic modeling to predict the hydrogen sulfide (H_{2}S) solubility in aqueous monoethanolamine (MEA), Nmethyl diethanolamine (MDEA), and diethanolamine (DEA) solution. For this goal, we used an electrolyte version of the Cubic Plus Association (eCPA) equation of state (EoS), wherein the molecular part of the EoS is based on the Soave–Redlich–Kwong (SRK) plus association EoS. We consider both water and alkanolamines as solvents. Thermodynamic properties of electrolyte solutions are expressed via chemical potentials and activity parameters of the species. Due to ionic interaction between the ions in the liquid phase, the answers are presumed to be nonideal. The proposed EoS contains six terms, including repulsive forces, shortrange interactions, association, long and short ranges ionic interactions, and the born term. In particular, the double interaction parameters between molecules and ionic types are optimized by the IL design (computeraided ionic liquid design, known as CAILD) model using MATLAB. A comparison is drawn between the outcomes of the proposed model and the experimental data obtained in this study, and data reported by other authors. The proposed model can wisely anticipate equilibrium treatment of H_{2}S absorption in aqueous MDEA, MEA, and DEA solutions in wide temperatures, acid gas loadings, pressures, and aqueous alkanolamine concentrations.
The significance of the results of the work is that it provides valuable information on the solubility of hydrogen sulfide (H_{2}S) in aqueous solutions of different alkanolamines (MDEA, MEA, and DEA). The investigation focused on the vaporliquid equilibrium of ternary systems and formulated a predictive model for H_{2}S solubility. A comparison between the experimental results and existing literature data was performed, revealing a commendable level of agreement between the proposed model and the experimental findings. The model possesses the capability to predict with precision the equilibrium treatment of H_{2}S absorption under diverse circumstances, encompassing a broad range of temperatures, acid gas loadings, pressures, and aqueous alkanolamine concentrations. This research is relevant in the field of gas sweetening processes, where the removal of H_{2}S from natural gas is crucial. Understanding the solubility of H_{2}S in alkanolamine solutions is essential for designing and optimizing gas sweetening processes.
Previous investigations have employed diverse models to forecast the solubility of H_{2}S. However, the model proposed in this study distinguishes itself by its remarkable capability to accurately anticipate solubility in an extensive array of circumstances. This encompasses a wide spectrum of temperatures, acid gas loadings, pressures, and aqueous alkanolamine concentrations. Furthermore, the data acquired through experimental means in this research exhibited an acceptable validation when compared to the outcomes of modeling endeavors. This further substantiates the efficacy of the aforementioned model. Overall, the proposed approach has the potential to optimize gas treating processes and reduce the environmental impact of acid gas emissions, making it a significant contribution to the field of gas treating.
Experimental
Chemicals
The chemicals MDEA, DEA, MEA, and H_{2}S were analytical grade and used from commercial suppliers without further distillation. The CAS numbers, suppliers, and other properties of the chemicals are listed in Table 1.
Table 1: CAS registry number, mass fraction purity, and main properties of the chemicals used in this study
Chemical name 
Chemical formula 
CAS number 
Suppliers 
Purity (wt. frac.) 
Appearance 
Density (g.cm^{3}) 
Molar mass (g.mol^{1}) 
MDEA 
CH₃N(C₂H₄OH)₂ 
105599 
Merck 
≥ 0.99 
Colorless liquid 
1.038 
119.166 
DEA 
HN(CH₂CH₂OH)₂ 
111422 
Merck 
≥ 0.995 
Colorless crystal 
1.095 
105.136 
MEA solution 
CH_{3}NH_{2} 
74895 
Sigma Aldrich 
0.4 in water 
Colorless liquid 
656.35 
31.055 
Hydrogen sulfide 
H_{2}S 
7783064 
Air Liquide 
0.99 
Colorless gas 
1.363 
34.08 
Apparatus and procedure
The experimental setup which was prepared in this study is a basis for the static procedure for the determination of the hydrogen sulfide solubility in aqueous solutions of NMethyldiethanolamine, diethanolamine, and methylamine [29].
Figure 1 demonstrates a schematic diagram of the apparatus setup. The equilibrium cell with a volume of 260 cm^{3} was made of Hastelloy material to refrain from corrosion problems and was immersed in an oil bath. The cell was operated at pressure ranges of more than 10 MPa and a temperature range between 323.15 and 473.15 K. Stirring rotors were employed to ensure the homogeneity of the two phases, including liquid and or vapor. A Pt100 thermocouple (Omega Company, United Kingdom) was employed to measure temperature with an accuracy of 0.01 K. The operating pressure was measured with a P8AP Pressure Transducer (Intro Enterprise Company, Thailand) with an accuracy of 0.0025 MPa. Hydrogen sulfide is used in the equilibrium cell from reserve flacons bathed in a thermostatic liquid bath. The bath was used to precisely estimate the operating temperature and pressure. Connecting lines were heated to hamper condensation problems. The proportion of the acid gas used in the equilibrium cell was estimated by considering the pressure and temperature conditions in the reserve flacons. A certain amount of the solvent solution by weight was employed in the equilibrium cell. Degassing was performed by a frigorific technique. Thereafter, the cell was heated at the desired temperature and the bubble point pressure of the pure solvent. Hydrogen sulfide of the storage bottles was added step by step. The cell equilibrium state time was about 50 min. It should be acclaimed that the total pressure was measured after injecting the acid gas.
Figure. 1: Schematic diagram of the experimental setup used in this study; (1) equilibrium cell, (2) liquid temperature equalizer, (3) solvent reserve flacon, (4) cell, (5) stirrer, (6) pressure indicatorthermometer, and (7) H_{2}S reserve flacon
Modeling
Thermodynamic framework
Chemical equilibrium
The absorption of acid gases by alkanolamines involves chemical reactions. To calculate the molar solubility of acid gas in alkanolamine, the first step is to compute the mole fractions of types (both molecules and ions) in the liquid phase. For the system of H_{2}O H_{2}Salkanolamin, the following main reactions occur [12]:
Ionization of water (water dissociation):
2H_{2}O H_{3}O^{+}+OH^{ } (1)
dissolved H_{2}S Ionization:
H_{2}O + H_{2}S H_{3}O^{+ }+ HS^{} (2)
amine Protonation:
RR'R"N+H^{+} RR'R"NH^{+ } (3)
Amine's Overall reaction:
RR'R"N+H_{2}S RR'R"NH^{+}+HS^{} (4)
Where R, R', and R" represent MDEA, MEA, and DEA solutions, respectively. The above reactions are proton transfer reactions in the liquid phase, which occur too quickly, except for response (3). It is reasonable to assume that the reactions (1), (2), and (4) are spontaneous. In industrial conditions, reaction (3) is selected because this reaction has a significant dissociation factor. According to the reactions (1) to (4) in the absorption process of H_{2}S by alkanolamines, the adsorbed H_{2}S is initially present in the form of an ion in an aqueous solution. The total concentration of H_{2}S will not be greater than the alkanolamine concentration. Equilibrium is between unreacted H_{2}S, which remains in molecular form in the liquid phase, and the same molecules in the vapor phase. So, if the H_{2}S partial pressure is known, the solubilities of H_{2}S in all states, i.e. molecular and ionic forms, significantly increase in aqueous alkanolamine solutions relative to the solubilities of these solutes in pure water owing to the dissociation of acid gases and protonation of the alkanolamines. This phenomenon may also be viewed from the reverse viewpoint. At a given apparent acid gas concentration (it is assumed that the electrolytes do not dissociate) in an aqueous alkanolamine solutions, the acid gas partial pressure in equilibrium with the answers will be significantly reduced relative to the acid gas partial pressure in equilibrium with pure water at the same loading of acid gas in the liquid phase.
Mole balance and charge equations in the liquid phase are as follows:
Mole balance for water:
Where, is the hydrogen sulfide loading equal to the mole ratio of absorbed hydrogen sulfide per amine, and n is the total mole number. , n_{RR'R"N,0}, and are initial moles of water, methyl diethanolamine, and hydrogen sulfide, respectively. They can be calculated at a given hydrogen sulfide loading and alkanolamine weight percent as follows:
Where, wt is the weight percent of alkanolamines and MW is the molecular weights.
Chemical equilibrium constants of reactions (1) to (4) are dependent on mole fractions of the species present in the responses as well as temperature and are expressed as follows [30]:
K_{j}= =exp(C_{j}^{(1)}+C_{j}^{(2)}/T+C_{j}^{(3)}ln(T))+C_{j}^{(4)} j=1,…,4 (12)
Where, x_{i}, , are mole fraction, activity coefficient, and the stoichiometric coefficient of species i in reaction j, respectively, T is the system's temperature. All the coefficients, including C^{(1)}, C^{(2)}, and C^{(3)} for each reaction, are given in Table 2 [31].
Table 2: Values of the coefficients presented in Equation (12)
Equation 
C_{j}^{(1)} 
C_{j}^{(2)} 
C_{j}^{(3)} 
C_{j}^{(4)} 
Temperature range (°C) 
Ref. 
(1) 
132.899 
13445.9 
22.4773 
0 
0225 
11 
(2) 
214.582 
12995.4 
33.5471 
0 
0150 
11 
(3) 
32.0 
3338 
0 
0 
1470 
12,13 
(4) RR'R"N= MDEA 
9.4165 
4234.98 
0 
0 
2560 
15 
(5) RR'R"N= MEA 
2.1211 
8189.38 
0 
.007484 
050 
16 
(6) RR'R"N= DEA 
6.7936 
5927.65 
0 
0 
050 
17 
The symmetrical activity coefficient for water is calculated according to the following equation [32]:
Where, T and P are temperatures, and total pressure of the system, and φ is the fugacity coefficient. Subscript 0 denotes the reference state. For the other types, unsymmetrical activity coefficients are calculated as follows [33]:
Where, subscript i refers to all species except water and superscript ∞ denotes the reference state of limited dilution in water. In this work, the fugacity coefficients of molecules and ions are determined with an appropriate eCPA.
According to Equation (12), for reactions 14, four equations could be written. These equations and also Equations 58 form a nonlinear equations system that should be dissolved simultaneously to calculate the mole fractions of all types (molecules and ions) which are presented in the liquid phase. Smith and Missen [34] proposed a method to dissolve this nonlinear equation system which is very complicated. Instead, we employed the Jacobian method as a simpler one with relatively low errors to solve the equations [35]. The Jacobian approach for obtaining thermodynamic derivatives is expanded. Any partial second derivative can be conveyed in terms of two sets of reference derivatives basis on the insufficient parameters (V, T) and (P, T), respectively. This method is given for the polyatomic ideal and van der Waals gases, blackbody radiation, and the general (relativistic and nonrelativistic) quantum gas. Ultimately, the classical theory of thermodynamic variation is expanded using Jacobians. Available formularies are obtained, which explicitly give the total fluctuation, partial fluctuation, and covariance of the instability of any thermodynamic parameter from its equilibrium value.
eCPA equation of state
The EOS is an essential tool when studying the thermodynamic properties and phase behavior of materials. Models used for the electrolyte solutions express the nonideality of electrolyte solution, and they are usually presented in terms of the Gibbs energy. Sadegh et al. [36] have contradicted the UNIQUAC model and a few models reported in the literature for the H_{2}S–MDEA–H_{2}O system. PCSAFT EoS has also been used to model the acid gas solubility in ethanolamine solutions [37]. A few models have been reported in terms of the Helmholtz energy. The EOS used in this study is the basis of the study conducted by Fürst and Renon [24] with an association term plus the Born term. The Helmholtz energy equation is expressed as follows:
Where, is the residual Helmholtz energy, equivalent to the disparity between the actual Helmholtz energy and ideal Helmholtz energy, these equations of states are included in six terms: repulsive forces (RF), shortrange interaction (SR1), association (Asso.), shortrange ionic interaction (SR2), and largerange ionic interaction (LR), and the Born terms. The first three terms are related to molecules, and the next three are attributed to ionic species. The shortrange interaction (SR1) and repulsive forces (RF) terms are usually related to the cubic equation of state. In this work, the SRK EoS is used as an appropriate cubic EOS. This equation, which can be utilized for both liquid and vapor phases, has several advantages. For example, it can be reduced to the cubicplusassociation equation of state if there are no ionized species in the liquid phase. As there is no association molecule, this equation of state can be reduced to the cubic EOS. Therefore, it can be utilized for various systems in refinery processes. Here, the SRK EoS is expressed as follows [38]:
Where, υ, R, and T are the molar volume of the mixture, the universal gas constant, and temperature, respectively, and a and b are the parameters of the SRK EoS. a(T) is calculated from the following equation:
Regarding the mixtures, the parameters a and b are calculated by appropriate mixing rules. In this work, the famous van der Waals mixing directions are adopted [39]:
Where, k_{ij} is a binary interaction coefficient specific to each binary pair in the mixture, the association term is expressed as follows [40]:
Where, x_{j} shows the mole fraction of molecular types, and M_{j} indicates the number of association sites in molecule j. X^{Aj} represents a fraction of A sites in molecule j that does not bond with other active bonds and is expressed as follows [41]:
where, shows the molar density and ^{AB} indicates association strength that expresses as follows [42]:
Where, and ^{AiBj} show association energy and volume, respectively. g(ρ) is the radial distribution function that is estimated as follows:
Where, η is calculated from the following equation:
Where, b is calculated from the mixing rules mentioned above.
In this work, parameters a_{0}, c_{1}, b, , and ^{AiBj} for the molecules are adopted from literature and given in Table 3 [43].
Table 3: Parameters of pure components in eCPA EoS [50]
DEA 
MEA 
MDEA 
H_{2}S 
H_{2}O 
Parameters 
715 
638 
677.8 
373.2 
647.30 
T_{c} 
105.14 
61.08 
119.16 
34.08 
18.02 
MW 
4.92 
3.7 
4.5 
3.49 
2.52 
( ) 
5.953 
17.5544 
8.17 
2 
19.29 
d^{(0)} 
9277 
14836 
8.99 10^{3} 
0 
2.98 10^{4} 
d^{(1)} 
0 
0 
0 
0 
1.97 10^{2} 
d^{(2)} 
0 
0 
0 
0 
1.32 10^{4} 
d^{(3)} 
0 
0 
0 
0 
3.11 10^{7} 
d^{(4)} 
4c 
4c 
4c 
4c 
4c 
Type of association 
2.0942 
1.4112 
2.1659 
0.396977 
0.12277 
a_{0}(pa.m^{6}.mol^{2}) 
1.5743 
0.7012 
1.3371 
0.53703 
0.667359 
C_{1} 
9.435 10^{5} 
5.656 10^{5} 
0.111 10^{3} 
2.950 10^{5} 
1.455 10^{5} 
b 
0.16159 
0.18177 
0.16159 
3726.34 
0.16655 
(pa.m^{3}/mol) 
0.0332 
0.00535 
0.0332 
0.04745 
0.0692 

For the mixtures, parameters and ^{AiBj} are determined via appropriate combination rules. There are several combination rules in the literature. The most common combination rule which is used in this study is CR1. It is defined by the following equations [44]:
In this study, for all of the present molecules, 4C (one of the association types) was used as the association type. This is the best type of association and has a minimum error compared to the other types [45,46].
The SR2 term expresses as follows:
Where, W_{ij} is an interaction parameter between ionion and moleculeion, in this work, according to Fürst and Renon [24], just interactions among cationsanions (W_{ca}) and the interactions among cations molecules (W_{cm}) were considered. The interactions between anion–anion (W_{aa}) and cation–cation (W_{cc}) was not considered due to the repulsive forces. Also, the interactions between anionsmolecules (W_{am}) were not considered due to the scarce salvation of anions. According to this model, it is supposed that ionic binary interaction (W_{ij}) is independent of temperature. ξ_{3} is the packing factor that is given by the Equation (29):
Where, i is related to all species, such as molecules and ions, the Avogadro’s number is shown by N_{A} and is the diameter of the molecule or ion. The diameter of species H_{2}O, OH^{}, and H_{3}O^{+} are chosen from Zoghi and Feyzi [25]. The diameter of molecules including H_{2}S, MDEA, MDEAH^{+}, MEA, MEAH^{+}, DEA, and DEAH^{+} are adopted from Chunxi and Fürst [47], which presented a method for calculating the diameter of ions. We used this method to calculate the diameters of HS^{ }and S^{2} as follows:
Where, ba is a parameter of b for anion, is anionic Pauling diameter, and fit parameters for eCPA EoS. The anion diameter calculates as follows:
Where, and are 1.6×107 and 3.005×106, respectively. parameter for two anions, HS^{} and S^{2}, are 3.6 and 3.68, respectively.
The term of largerange ionic interaction (LR) in Equation (15) is described by the streamlined MSA model as follows:
Where, parameter z is the ion charge and is a Shielding parameter, is a dielectric constant of the system. and are expressed as follows [48]:
Where, is calculated from Equation (29), but the summation is only on ionic species. is the vacuum electric permittivity (in terms of C2 J^{−1} m^{−1}) and the parameter e is electron charge (1.60219 × 10^{−19}) in unit of (C). D_{s} is the dielectric constant which is expressed as follows [49]:
Where, the summation is only on the molecules. Dielectric constants of pure species are defined as a subordinate of temperature by:
Dm=d^{(0)}+d^{(1)}/T+d^{(2)}T+d^{(3)}T^{2}+d^{(4)}T^{3} (37)
Parameters d^{(0)} through d^{(4)} are given in Table 3.
In Equation (33), parameter is obtained using a NewtonRaphson technique. The Born term is obtained by the next equation:
The Born term is a strong subordinate of the Dielectric constant of the solvent and is used as a correction factor for the normal state of ions. The Born term is not used to calculate the activity coefficient of ions in the systems, including a pure solvent (such as pure water). This term is used only for mixed solvents when pure water with limited dilution is used as a reference state for the ionic types. In other words, the Born term is used to consider the effects of mixed solvents.
3.3. Phase Equilibrium
The fundamental relation describing the vaporliquid equilibrium is:
Where, and show i component fugacity in phases of vapor and liquid, respectively. The fugacity of components often determines by the fugacity coefficient and the above equation can be rewritten in the form of the fugacity coefficient as next equation:
Where, and are the fugacity coefficients of component i in the vapor and liquid phases, respectively. We used the eCPA Eos to determine the fugacity coefficients. i component mole fractions in liquid and vapor phases are shown by x_{i} and y_{i}, respectively.
Physicalchemical equilibrium
Generally, both phase physical and chemical equilibrium calculations are required to design gas treating processes. Phase equilibrium sets out the required driving force for mass transfer in the absorption system. In an absorption system of acid gas by alkanolamines in the liquid phase, many reactions occur; therefore, chemical equilibrium should be considered in a thermodynamic model. In this work, the ion species exist in the liquid phase due to their nonvolatile exclusivity. So, there are only three molecules, including H_{2}O, MDEA, and H_{2}S, in the vapor phase.
Model for alkanolamine increment in H_{2}OH_{2}S system
The calculation is started by assuming initial pressure. First, the computation is performed with the given temperature and acid gas loading mole fractions of all types, such as liquid phase molecules and ions, by the mathematical Jacobian algorithm [45]. Second, the bubble point pressure calculation algorithm obtains the mole fractions. The calculation outputs are the mole fractions and the bubble pressures of molecular components in the vapor phase. All calculations are repeated with these obtained pressures. The estimates continue until the difference between two consecutive pressures will be less than an assumed tolerance (ɛ).
In this study, to raise the accuracy of the model, in addition to considering three molecules of H_{2}O, H_{2}S, and alkanolamine, five ions ( H^{+}, H_{3}O^{+}, HS^{}, S^{= },^{ }and OH^{}) are also considered in the liquid phase according to the method of Zoghi and Feyzi [25]. There are also three binary interactions between molecules (k_{ij}) and also five moleculeion and ionion binary interaction parameters (w_{ij}). The experimental data were used for fitting the binary interaction parameters. In this study, the following objective function (O.F.) has been used.
Where, P_{expi} and P_{cali}_{ }are experimental and calculated pressures, respectively, the predicted correlations from bubble pressure calculations in the systems of H_{2}OH_{2}SMDEA, H_{2}OH_{2}SMEA, and H_{2}OH_{2}SDEA for adjusted parameters of k_{ij} and w_{ij} as functions of temperature are shown in the following: Note that the species H_{2}O H_{2}S RR'R"N RR'R"NH^{+} H_{3}O^{+} HS^{} S^{2} OH^{}are named 18, respectively.
H_{2}OH_{2}SMDEA system (n_{p} = 86 and AAD% = 13.2):
k_{12} = 2E08T^{4} + 3E05T^{3}  0.0183T^{2} + 4.4819T  410.78
k_{13} = 2E08T^{4} + 2E05T^{3}  0.0129T^{2} + 3.0603T  272.12
k_{23} = 3E08T^{4} + 4E05T^{3}  0.0221T^{2} + 5.3431T  481.32
w_{34} = 3E11T^{4}  4E08T^{3} + 2E05T^{2}  0.0054T + 0.4942
w_{14} = 2E11T^{4} + 3E08T^{3}  2E05T^{2} + 0.004T  0.3593
w_{24} = 0.0001
w_{64} = 3E11T^{4} + 4E08T^{3}  2E05T^{2} + 0.0054T  0.494
w_{74} = 0.0001
H_{2}OH_{2}SMEA system (n_{p} = 38 and AAD% = 21.57):
k_{12} = 3E08T^{4} + 4E05T^{3}  0.0196T^{2} + 4.0997T  317.54
k_{13} = 6E08T^{4} + 8E05T^{3}  0.0393T^{2} + 8.5004T  685.18
k_{23} = 9E08T^{4} + 0.0001T^{3}  0.0602T^{2} + 13.533T  1134.9
w_{34} = 2E10T^{4} + 3E07T^{3}  0.0001T^{2} + 0.0294T  2.4233
w_{14} = 9E11T^{4}  1E07T^{3} + 7E05T^{2}  0.0153T + 1.3301
w_{24} = 2E10T^{4} + 3E07T^{3}  0.0002T^{2} + 0.0376T  3.1327
w_{64} = 2E09T^{4} + 3E06T^{3}  0.0014T^{2} + 0.315T  26.55
w_{74} = 6E10T^{4}  9E07T^{3} + 0.0005T^{2}  0.1094T + 9.6381
H_{2}OH_{2}SDEA system (n_{p} = 40 and AAD% = 21.24):
k_{12} = 0.0003T^{2}  0.2048T + 36.202
k_{13} = 0.0003T^{2}  0.2117T + 38.1
k_{23} = 1
w_{34} = 3E06T^{2}  0.0021T + 0.3606
w_{14} = 1E07T^{2} + 0.0001T  0.0184
w_{24} = 4E07T^{2}  0.0003T + 0.0498
w_{64} = 4E06T^{2}  0.0027T + 0.4679
w_{74} = 4E07T^{2}  0.0003T + 0.0447
Results
Preliminary experimental results
Figure 2 shows the experimental and modeling results of the evaluation of H_{2}S solubility in three systems, including MEAH_{2}OH_{2}S, MDEAH_{2}OH_{2}S, and DEAH_{2}OH_{2}S obtained in this study. We reported H_{2}S partial pressures as a subordinate of H_{2}S loading in a constant concentration of alkanolamines at different temperatures. According to Figure 2, the numerical modeling results were validated by the experimental tests for various temperatures. Comparisons between the outcomes of the proposed model with the experimental data reported in the literature are shown in Figures 35, where the partial pressures of H_{2}S as a subordinate of H_{2}S loading in a constant amount of alkanolamine at the various temperatures are demonstrated. As the H_{2}S loading increases, the curves get away from each other. When the temperature increases, the slope of the curve enhances. At the constant H_{2}S loading and the constant concentration of alkanolamine, the partial pressure of H_{2}S grows by increasing temperature. At the low H_{2}S loading, the temperature has not a considerable effect on the H_{2}S partial pressure. In other words, at the constant alkanolamine weight concentration and the low H_{2}S loading, the partial pressure of H_{2}S remains the same with increasing the temperature.
Figure 2: A comparison among the outcomes of our model and the experimental data collected in this study for solubility of H_{2}S in alkanolamines aqueous solution; (a) 21 wt.% MDEA at 323.15 K, (b) 14 wt.% MEA at 323.15 and 343.15 K, and (c) 23.3 wt.% DEA at 333.15 K
Hydrogen sulfide can reply immediately with DEA, MDEA, and MEA over a regular acidbase interaction. Simultaneously, the water's existence would raise the acid gas uptake through the dissolution of hydrogen sulfide and the protonation of the amine. Hence, we can recognize two feasible approaches through which H_{2}S is absorbed; the first mechanism immediately into the amine and the other one by water. Furthermore, the absorption of hydrogen sulfide in the amine H_{2}O system can be considered a consequence of both chemical and physical absorptions. Thus, to organize a good argument about the behavior observed in Figures 35, the physical absorption of hydrogen sulfide into amine H_{2}O systems should be considered. This can also be proved by noticing the slope of indicative tendency curves in Figures 35. The slope indicates the systems absorption capacity. It can be detected that the Px curve has a lower slope as the amine composition surges. The linearity increases as the slope decreases, and thus physical absorption increases. This behavior is also pursued when the pressure increases to a higher amount. In conditions with low temperatures like our investigated temperature of 283 K, these influences could not be discernible since the absorption capacity is very high.
Figure 3: A comparison between the results of the model and the experimental data for solubility of H_{2}S in aqueous solution of MDEA reported by [55]; (a) 23.3 wt.% solution at 313.15 and 373.15 K and (b) 48.8 wt.% solution at 313.15 K
Figure 4: A comparison between the results of our model and the experimental data for solubility of H_{2}S in aqueous solution of MDEA reported by [57]; (a) 23.3 wt.% solution at 313.15 and 333.15; (b) 18. 68 wt.% solution at 373.15, 393.15, and 413.15 K
In Figure 6, the H_{2}S partial pressure is plotted as an H_{2}S loading subordinate at a constant temperature and the various alkanolamine weight concentrations. As the alkanolamine weight concentration increases, the slope of the curve enhances. At the low H_{2}S loading, alkanolamine attention had a more negligible effect on the H_{2}S partial pressure. At the constant temperature and the constant H_{2}S loading, the amount of H_{2}S partial pressure increases with enhancing the alkanolamine concentration.
In Figure 7, the ratios of equilibrium experimental H_{2}S partial pressure to equilibrium calculated H_{2}S partial pressure are plotted versus H_{2}S loading in the systems H_{2}OH2SMEA, H_{2}OH_{2}SMDEA, and H_{2}OH_{2}SDEA. At high temperatures and very low H_{2}S loading, there is a systematic experimental error. Therefore, the calculated pressures seem scattered. As the amount of H_{2}S loading increases, the ratio of equilibrium practical H_{2}S partial pressure to equilibrium calculated H_{2}S partial pressure is approached 1.
Figure 5: A comparison among the outcomes of our model and the experimental data for solubility of H_{2}S in aqueous solution of alkanolamines; (a) 15.27 wt.% MEA solution at 298.15, 313.15, 333.15, 353.15, and 393.15 K [58], (b) 36.799 wt.% DEA solution at 323.15 and 373.15 K [59], and (c) 25 wt.% DEA solution at 339 K [60]
Figure 6: A comparison among the outcomes of our model and the experimental data for H_{2}S solubility in MDEA aqueous solution; (a) 23.3 and 48.8 wt.% solution at 313.15 K [57,58] and (b) 23.3 and 18.68 wt.% solution at 373.15 K [54, 55]
The results of hydrogen sulfide solubility in aqueous solutions of MEA, MDEA, and DEA using eCPA EoS obtained from the experimental evaluation were compared with the results obtained from modeling, as demonstrated in Figure 8. Results showed good agreement between those data. To assess the validity of the predicted model, we used the absolute average relative deviation (AARD%) as a statistical errorindex, defined by:
Where, X is the solubility of H_{2}S, M is the data points’ number, and the experimental data and calculated solubility values are shown by the ‘exp’ and ‘cal’ subscripts. Table 4 illustrates the importance of AARD% in the H_{2}S solubility of the mentioned systems. The results obtained from the predicted model exhibited excellent agreement with our data.
Figure 7: The ratio of experimental to calculated H_{2}S partial pressure; (a) MDEA solution: data (♦) from [61], data (n) from [55], and data (▲) from [54], (b) 15.27 wt.% MEA solution [58], and (c) DEA solution: data (♦) from [59], data (n) from [60]), and data (▲) from [59]
Figure 8: A comparison of the computed and the experimental data for H_{2}S equilibrium partial pressure over aqueous (a) MDEA, (b) MEA, and (c) DEA solutions
Table 4: The calculated absolute average relative deviation (AARD%) in the H_{2}S solubility of the MDEAH_{2}OH_{2}S, MEAH_{2}OH_{2}S and DEAH_{2}OH_{2}S systems
Concentration of aqueous solution 
T (K) 
P_{H2S }(exp) × 10^{3} (MPa) [51] 
P_{H2S} (PCSAFT) ×10^{3} (MPa) [51] 
AARD % 
P_{H2S} (ePC_SAFTMB), MPa ×10^{3} [51] 
AARD % 
30 wt. % MDEA 
313 
14.04 
27.57 
55.08 
22.45 
38.88 
29.17 
58.33 
46.17 

59.46 
101.07 
80.93 

128.2 
151.80 
127.93 

229.6 
189.99 
168.93 

330.6 
215.54 
199.47 

445.7 
228.40 
215.81 

30 wt. % MDEA 
373 
20.11 
27.83 
31.45 


40.74 
64.29 



90.13 
143.73 



131.9 
167.09 



191.0 
232.05 



295.5 
273.42 



348.0 
317.32 



Concentration of aqueous solution 
T (K) 
P_{H2S }(exp) × 10^{3} (MPa) [52] 
P_{H2S} (emPRCPA) × 10^{3} (MPa) [52] 
AARD % 

32.2 wt. % MDEA 
313 
15.91 
26.01 
39.71 

31.04 
49.73 

61.33 
84.49 

130.07 
131.49 

231.47 
172.49 

332.47 
203.03 

447.57 
219.37 

Concentration of aqueous solution 
T (K) 
P_{H2S }(exp) × 10^{3} (MPa) [53] 
P_{H2S} (PCSAFT) × 10^{3} (MPa) [53] 
AARD % 

15.3 wt. % MEA 
333 
5053.76 
4659.5 
4.37 

5232.97 
4910.39 

5913.98 
5555.56 

6523.3 
6344.09 

7240.14 
7025.09 

7598.57 
7562.72 

Concentration of aqueous solution 
T (K) 
P_{H2S }(exp) × 10^{3} (MPa) [53] 
P_{H2S} (PCSAFT) × 10^{3} (MPa) [54] 
AARD % 

25 wt. % DEA 
394.26 
3748.99 
3524.25 
1.42 

4881.9 
4881.9 

6497.55 
6385.47 

6607.41 
6719.5 

7085.67 
7086.23 

7854.65 
7856.88 

8113.21 
8150.94 

Concentration of aqueous solution 
T (K) 
P_{H2S }(exp) (MPa) [55] 
P_{H2S} (Present model), (MPa) [55] 
AARD % 

15.27 wt. % MEA 
353.15 
0.0235 
0.0152 
15.42


0.0869 
0.0538 

0.143 
0.1604 

0.316 
0.382 

0.853 
0.8449 

1.307 
1.298 

1.802 
1.819 

25 wt. % DEA 
339 
0.01017 
0.00598 
24.53 

0.01427 
0.00799 

0.01834 
0.00788 

0.02244 
0.0119 

0.02856 
0.0139 

0.03684 
0.02009 

0.04094 
0.03047 

0.04928 
0.0325 

0.06588 
0.04495 

0.07208 
0.0636 

0.08456 
0.07618 

0.10123 
0.0970 

0.12420 
0.1200 

0.15135 
0.1471 

0.21402 
0.2203 

0.28092 
0.2914 

0.38970 
0.3959 

23.3 wt. % MDEA 
373.15 
P_{H2S }(exp) (kPa) [56] 
P_{H2S} (Present model), (kPa) [56] 
AARD % 

24.7506 
8.17001 
28.26 

28.3689 
11.7883 

40.6287 
19.8813 

81.4691 
85.5878 

147.349 
147.32 

283.468 
275.153 

498.361 
431.99 

Concentration of aqueous solution 
T (K) 
P_{H2S }(exp, present work) (MPa) 
P_{H2S} (Present model), (MPa) 
AARD % 

21 wt. % MDEA 
323.15 
2.61129 
2.60373 
2.29 

3.81315 
3.77709 

6.77583 
6.82177 

8.74297 
8.69562 

9.25599 
9.17492 

10.7137 
10.5686 

13.3491 
12.9161 

13.7759 
13.9266 

18.7838 
18.2387 

26.0152 
27.4282 

32.3329 
34.8698 

14 wt. % MEA 
323.15 
0.015152 
0.015025 
4.23 

0.01865 
0.01894 

0.020614 
0.019938 

0.028265 
0.029271 

0.052703 
0.051609 

0.198759 
0.181464 

0.797691 
0.721136 

23.3 wt. % DEA 
333.15 
7.7541 
7.9147 
3.45 

12.15254 
11.63181 

19.264 
18.9178 

38.76458 
39.93175 

65.437 
63.27355 

81.179 
77.61565 

121.506 
130.6538 

249.436 
256.8715 

351.504 
357.447 
Discussion
As evident from Figure 2, the computed results have acceptable obedience with our experimental data in temperatures of 313343 K and MDEA, DEA, and MEA concentrations of 0.20.7, 0.30.9, and 0.21.2 wt. %, respectively, which shows satisfactory forecast strength of the suggested model. Despite the simplicity, the proposed model may be more accurate than PCSAFT EoS and ePCSAFT EoS forecast H_{2}S solubilities in aqueous MDEA, DEA, and MEA in wide temperature ranges concentrations. Figures 28 and Table 4 provide comparative information among the outcomes obtained by the PCSAFT EoS, ePCSAFT EoS, emPRCPA EoS, the suggested model, the obtained experimental data, and the experimental data reported in the literature for a variety of MDEA, DEA and MEA concentrations and temperatures. The values of AARD%s for PCSAFT EoS, ePCSAFT and emPRCPA EoS are less than 97 %, 60 %, and 64 %, respectively. These results demonstrate that merging electrolyte terms, i.e. Born and MSA, amends the accuracy of the equation of state due to the presence of ionic liquids in the solution. Table 4 also shows more accuracy in the PCSAFT prediction of DEA concentrations compared to MEA and MDEA concentrations. According to the published experimental data and the comparison with the proposed model, the model developed in this study shows more accuracy in the 25 wt. % DEA solution. The highest deviations of the published experimental H_{2}S solubility data from the proposed model are 15.27 wt. % MEA solution and 353.15 K. The published experimental H_{2}S solubility data has had the highest agreement and the lowest AARD % with the proposed model compared to the other EoSs. The results of our experimental data demonstrate a satisfactory agreement with the prosed model. The highest AARD % of our data and the proposed model for MDEA, DEA, and MEA solutions are 7.84 %, 7.5 %, and 8.7 %, respectively. Development in the accuracy of modeling results was observed by comparing our experimental data points and the published experimental data points.
Conclusion
In this study, the vaporliquid equilibrium of ternary systems of hydrogen sulfide, water, MDEA, MEA, and DEA in a wide range of pressures (0.00263866.5 kPa), a temperature range of 313.15413.15 K, and the H_{2}S loading range of 0.07251.56 was investigated through both experiments and modeling to obtain the H_{2}S solubility in the aqueous MDEA, MEA, and DEA solutions. The modeling results of this paper were obtained using eCPA EoS and were contrasted with the outcomes attained from the PCSAFT EoS. For the nonelectrolytic part of the employed equations, the EoS proposed by Austgen et al. was used. Regarding water, alkanolamine, and hydrogen sulfide, the association term was considered in modeling studies. For the electrolytic part of the employed equations, the proposed model by Fürst and Renon plus the born time was used. The eCPA EoS used in this study has a prima facie error compared to other equations used in the literature. This is because most probable conditions such as hydrogen bonds, reactions, and the presence of ionic species are considered in the modeling. The experimental equilibrium data are used for fitting the binary interaction parameters. The presented (previous) models were able to calculate the H_{2}S partial pressures with the average AARD of 95.4%, 24.5%, and 28.2% for MEA, DEA, and MDEA, respectively. However, the average deviations of the calculated results by our suggested model for MEA, DEA, and MDEA solutions were 4.2%, 3.4%, and 2.29%, respectively. Consequently, it can be stated that the experimental data obtained in this work had an acceptable validation with the results of modeling works. Optimization of aminebased gas sweetening processes, development of new solvents, modeling and simulation of gasliquid equilibrium, and alternative energy applications are some insights into potential future research directions stemming from this study.
Conflict of Interest
The authors state that they have no competing financial interests or known personal relationships that appear to affect the work described in this article.
List of Symbols
residual Helmholtz energy
cal calculated
DEA Diethanolamine
DGA Diglycolamine
eCPA Electrolyte Cubic Plus Association
EoS Equation of state
exp experimental
MDEA N methyldiethanolamine
MEA Monoethanolamine
P Pressure
RF Repulsive forces
R Universal gas constant
VLLE Vapor Liquid Liquid Equilibrium
SRK Soave–Redlich–Kwong
_{ }Activity coefficient of species i
Stoichiometric coefficient of species i
υ Molar volume of the mixture
Anionic Pauling diameter
T Temperature
 Weight concentration
x_{j} Mole fraction of molecular species
Fugacity coefficients of component i
g Gas phase
l Liquid phase
M_{j}_{ }Number of association sites in molecule j.
X^{Aj} Fraction of A sites in molecule j
ORCID
Abolfazl Mohammadi
https://orcid.org/0000000206234815
HOW TO CITE THIS ARTICLE
Fariborz Fazelipour, Shahin Alizadeh, Abolfazl Mohammadi*, Alireza Bozorgian. Hydrogen Sulfide Solubility in Aqueous Solutions of MDEA, MEA, and DEA: Bridging Theory and Experiment with eCPA Equation of State. Chem. Methodol., 2023, 7(12) 916943.